Motion in a Plane PYQs - Last 10 Years

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Practice 84 JEE Main Physics questions from Motion in a Plane. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Motion in a Plane Questions

Showing 34 of 84 filtered questions.

1Motion In A Plane

If the initial velocity in horizontal direction of a projectile is unit vector \(\hat{i}\) and the equation of trajectory is \(y=5 x(1-x)\). The \(y\) component vector of the initial velocity is ______________ \(\hat{j}\). ($$\mathrm{Take}$...

INTEGER+4 / -12022

2Motion In A Plane

Two projectiles thrown at \(30^{\circ}\) and \(45^{\circ}\) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

3Motion In A Plane

Two projectiles are thrown with same initial velocity making an angle of \(45^{\circ}\) and \(30^{\circ}\) with the horizontal respectively. The ratio of their respective ranges will be :

4Motion In A Plane

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R....

5Motion In A Plane

A ball is projected from the ground with a speed 15 ms\(-\)1 at an angle \(\theta\) with horizontal so that its range and maximum height are equal, then 'tan \(\theta\)' will be equal to :

6Motion In A Plane

A projectile is projected with velocity of 25 m/s at an angle \(\theta\) with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of \(\theta\) will be ...

7Motion In A Plane

A body is projected from the ground at an angle of 45\(^\circ\) with the horizontal. Its velocity after 2s is 20 ms\(-\)1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms\(-\)2)

INTEGER+4 / -12022

8Motion In A Plane

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

9Motion In A Plane

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30\(^\circ\) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \(\theta\) with the line AB should be ____...

INTEGER+4 / -12021

10Motion In A Plane

A player kicks a football with an initial speed of 25 ms\(-\)1 at an angle of 45\(^\circ\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms\(-\)2)

11Motion In A Plane

The trajectory of a projectile in a vertical plane is y = \(\alpha\)x \(-\) \(\beta\)x2, where \(\alpha\) and \(\beta\) are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of proje...

12Motion In A Plane

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

13Motion In A Plane

A butterfly is flying with a velocity \(4\sqrt 2\) m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

14Motion In A Plane

The ranges and heights for two projectiles projected with the same initial velocity at angles 42\(^\circ\) and 48\(^\circ\) with the horizontal are R1, R2 and H1, H2 respectively. Choose the correct option :

15Motion In A Plane

A person is swimming with a speed of 10 m/s at an angle of 120\(^\circ\) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is ___...

INTEGER+4 / -12021

16Motion In A Plane

A mosquito is moving with a velocity \(\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k\) m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?

17Motion In A Plane

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just o...

INTEGER+4 / -12021

18Motion In A Plane

A particle starts from the origin at t = 0 with an
initial velocity of 3.0 \(\widehat i\) m/s and moves in the
x-y plane with a constant acceleration
\(\left( {6\widehat i + 4\widehat j} \right)\) m/s2 . The x-coordinate of the
particle at ...

19Motion In A Plane

A particle is moving along the x-axis with its
coordinate with the time 't' given be x(t) = 10 + 8t – 3t2. Another particle is moving
the y-axis with its coordinate as a function of
time given by y(t) = 5 – 8t3. At t = 1s, the speed
of the ...

INTEGER+4 / -02020

20Motion In A Plane

A particle moves such that its position
vector \(\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j\) where \(\omega\) is a constant and t is time. Then which of the following statements is true for the ...

21Motion In A Plane

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with
speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further
increasing the speed of the car to (1 + $$\bet...

22Motion In A Plane

A balloon is moving up in air vertically above a
point A on the ground. When it is at a height h1,
a girl standing at a distanced (point B) from A
(see figure) sees it at an angle 45o with respect
to the vertical. When the balloon climbs up...

23Motion In A Plane

Starting from the origin at time t = 0, with initial velocity 5\(\widehat j\) ms-1 , a particle moves in the x-y plane
with a constant acceleration of \(\left( {10\widehat i + 4\widehat j} \right)\) ms-2. At time t, its coordinates are (20 ...

24Motion In A Plane

A particle is moving with a velocity
\(\overrightarrow v \, = K(y\widehat i + x\widehat j),\) where K is a constant.
The general equation for its path is :

25Motion In A Plane

The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos\(\omega\)t
y = a sin\(\omega\)t and
z = a\(\omega\)t
The speed of the particle is :

26Motion In A Plane

The stream of a river is flowing with a speed
of 2km/h. A swimmer can swim at a speed of
4km/h. What should be the direction of the
swimmer with respect to the flow of the river to
cross the river straight ?

27Motion In A Plane

Ship A is sailing towards north-east with
velocity \(\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop j\limits^ \wedge\) km/hr where \(\mathop i\limits^ \wedge\) points
east and \(\mathop j\limits^ \wedge\) , north. ...

28Motion In A Plane

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :...

29Motion In A Plane

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a
distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the
product ...

30Motion In A Plane

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2
. If it were launched at an
angle \(\theta\)0 with speed v0 then (g = 10 ms–2) :

31Motion In A Plane

Two particles are projected from the same point with the same speed u such that they have the same range R,
but different maximum heights, h1 and h2. Which of the following is correct ?

32Motion In A Plane

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the grou...

33Motion In A Plane

A plane is inclined at an angle \(\alpha\) = 30° with respect to the horizontal. A particle is projected with a speed u =
2 ms–1
, from the base of the plane, making an angle \(\theta\) = 15° with respect to the plane as shown in the figu...

34Motion In A Plane

A man in a car at location Q on a straight highway is moving with speed \(\upsilon\). He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that...